Corporate entities don’t have a billing issue (unless metering/charging for product support under some form of service contract).
Lawyers charge time spent on computer as they would on other correspondence or research.

Doctors need to be able to do the same. The problem is that present compensation is tied to face-to-face encounter time only.
That needs to be fixed and an acceptable payment arrangement needs to be created for doctors to be willing to spend professional time communicating with patients by email.

Doctors aren’t Luddites. Far from it. But they aren’t going to do more work for free just because email seems modern and convenient.
It’s work. There’s time and liability at issue. It needs to be paid for.